In power system operation, power generation schedules are built based on forecasted load. The objective is to ensure stable and economic operation. These schedules are part of an Energy Management System (EMS) that controls an entire energy system. Current EMS systems provided by vendors such as Siemens, ABB and Alstom, contain real-time economic dispatch functions that use methods such as the optimal power flow method.
One type of schedule is based on the Economic Dispatch (“ED”) model in which required power generation is allocated to a number of power generators to meet the varying load demand. The operating cost of the power system depends on the total fuel cost of these power generators. Therefore, the model seeks to allocate the load to the lowest cost generators. Thus, by finding the minimum optimal solution of the optimization functions that depend on the fuel cost, ED results in fuel cost saving.
Due to the highly nonlinear characteristics of power systems and generators, ED belongs to a class of nonlinear programming optimization problems that contain equality and inequality constraints, which are computationally hard to solve.
The conventional methods available for solving ED power system real-time economic dispatch problems mainly include the optimal power flow method (OPF) and the traditional participation factors method. The OPF method is generally effective to obtain optimal generation schedules. However, the execution speed is relatively slow in large systems.
Even after the schedules are created, they need to be adjusted if the actual load deviates from the plan. Such adjustments are also necessary if the outputs of renewable energy sources deviate from the forecasted value, and the fluctuation from renewable energy sources could be faster and heavier than loads.
As more renewable energy sources are deployed in power systems, the real-time economic dispatch method is becoming more uncertain because of the fast fluctuations caused by the loads and renewable power sources. As a result, algorithms that can adjust the generation schedules fast and efficiently are needed. The participation factor method could be used to find new optimal operating points after small deviations from the original plan, which is the base point. However, the participation factor method ignores the effect of transmission losses in the optimization process and the accuracy of the result may be poor.
The article by Guoyu et al, “Decoupled economic dispatch using the participation factors load flow,” IEEE Trans. Power App. Syst., vol. PAS-104, no. 6, pp. 1377-1384, June 1985, considers transmission losses in a participation factors method. However, in this article a first order approximation of transmission losses is adopted, which is much simpler and is still not very accurate. In the article by Abouheaf et al., “Dynamic formulation and approximation methods to solve economic dispatch problems,” Generation, Transmission & Distribution, JET, vol. 7, no. 8, pp. 866-873, August 2013, there is disclosed a method with a similar objective to the participation factor method, but the algorithm and modeling of transmission losses are different and the result is still not very accurate.
Thus, it would be advantageous if a method were provided that models transmission losses in a more precise way so that the result is much more accurate and it can be executed more quickly than the prior art.